A 3D reconstruction from 2D points
In this Python+Sagemath project, we reconstructed a complex 3d object from 2D points on a screen.
We used various numeric methods from algebra, like the least square difference or the approximated reduction of a matrix.
The final result is a 3D object that can be moved and rotated freely.
International Baccalaureate: Extended Essay
In my Extended Essay, I studied the foundations of Machine Learning from infinitesimal calculus.
I deduced the cost and output functions of a neuron from partial derivatives.
The network I programmed was capable of identifying dangerous asteroids for the earth with 99.1% efficiency
International Baccalaureate: Mathematical Exploration
I modelled precipitation return times (in Madrid) based on the Gamma distribution.
I mathematically demonstrated some of its most important properties. With the help of the Foster-Ribkin coefficients, I built a graph and confidence intervals for it.
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International Baccalaureate: Physics Report
In this essay, I studied the Magnus effect on a small spherical projectile fired at high speeds with rear rotation.
I came up with a system of differential equations that I didn't know how to solve at the time, but a linearization technique helped me find conclusive results.
Complex fractals with gnuplot
This essay studies the generation and representation of fractals from applying Newton's method of convergence in a space of R^2 that contains roots of imaginary polynomials. After creating several routines in C to evaluate polynomials and their derivatives, I wrote a code that allows to distinguish the areas of attraction graphically (gnuplot).